Low-lying eigenmodes of the Wilson-Dirac operator and correlations with topological objects

TL;DR

This paper investigates the relationship between low-lying eigenmodes of the Wilson-Dirac operator and topological objects in SU(3) gauge fields, revealing correlations through comparisons with topological charge and action density.

Contribution

It provides a detailed analysis of eigenvector properties and their correlation with topological features in both Monte-Carlo generated and instanton background fields.

Findings

Eigenvectors correlate with topological charge density.

Instanton models fit eigenmodes well.

Differences observed between hot and cooled fields.

Abstract

The probability density of low-lying eigenvectors of the hermitian Wilson-Dirac operator is examined. Comparisons in position and size between eigenvectors, topological charge and action density are made. We do this for standard Monte-Carlo generated SU(3) background fields and for single instanton background fields. Both hot and cooled SU(3) background fields are considered. An instanton model is fitted to eigenmodes and topological charge density and the sizes and positions of these are compared.